Intraocular Lenses (IOLs) are frequently used for restoring or improving visual performance, such as after cataract surgery. Because an IOL may be selected from various providers and in differing IOL powers, reliable systems and methods to select IOL powers to achieve the desired refractive outcome for a patient are needed. More particularly, it is most desirable to select an IOL power that will achieve emmetropia after surgery, independent of the refractive state or clinical history of the patient prior to implantation. The term emmetropia, and variations thereof, is used herein to indicate a state of vision in which an object at infinite distance from the subject eye is in sharp focus on the patient's retina.
The IOL power necessary to achieve emmetropia is often calculated using regression theory. One of the first calculations using this approach was the Saunders, Retzlaff, and Kraff formula (SRK). It is a regression formula empirically derived from clinical data to indicate the optimal power for an IOL. The SRK regression formula is:P=A−2.5*AXL−0.9*K 
where P is the IOL power, A is the lens constant, AXL is the axial length in millimeters, and K is the average corneal power in diopters. Unfortunately, the SRK regression formula may lead to the indication of a stronger IOL power for long eyes, and a weaker IOL power for short eyes. That is, the SRK typically underestimates the necessary IOL power to obtain emmetropia for short eyes, and overestimates the IOL power necessary for long eyes.
In order to remedy these shortcomings of SRK, the SRKII regression formula was developed, incorporating further empirical analysis of clinical data. In the SRKII regression, an additional constant is provided to modify the lens constant A from the SRK formula. The modification to A is based on whether the eye is long or short. More particularly, the SRKII formula is:P=A−2.5*AXL−0.9*K+F 
where F is a known constant that is equal to +3D at less than 20 millimeters of axial length (AXL), +2D at 20 to 20.9 millimeters, +1D at 21 to 21.9 millimeters, 0D at 22 to 22.5 millimeters, and −0.5D at greater than 24.5 millimeters. By way of example, if SRK yields an IOL power of +32D, SRKII may yield an IOL power of +35D (+32D+3D=+35D), if the patient's axial length is less than 20 mm.
An additional regression method, developed in an effort to address the shortcomings of SRK and SRKII, is the SRK/T formula. In the SRK/T method, the empirical calculation based on regressions is used to predict the position of the IOL in the eye after surgery. Once the position is known, the IOL power to implant is calculated by simple paraxial optics, taking into account that the eye can be modeled under this approximation as a two lens system (wherein the two lenses are the cornea and the IOL), focusing on the retina. This approach is based on Fyodorov's theoretical formula.
There are numerous formulas for calculating IOL power, such as the aforementioned, and additionally the Haigis, Olsen, and Holladay 1 and 2 models, for example. An in-depth analysis of IOL power calculation methods is provided in Shammas H J (ed.), Intraocular Lens Power Calculations, Thorofare, N.J.; Slack (2004), which is incorporated herein by reference as if set forth in its entirety.
However, it is well known that these formulas do not provide accurate predictions to achieve emmetropia for all preoperative refractive states. While a good prediction may be obtained using some of the aforementioned formulas to achieve emmetropia after surgery for emmetropic or close to emmetropic patients prior to surgery, errors arise for those with extreme myopia or hyperopia. These deviations for extreme eyes are not unexpected, because empirical regressions have been back calculated from “average,” that is, emmetropic or near-emmetropic, eyes. Due to the regression nature of these formulas, even emmetropic eyes with a non common or odd configuration may not be well predicted, since they are not inside of the regression. Thus, it is also possible to have errors in emmetropic eyes.
For example, FIG. 1 illustrates the variations from the predicted outcome, for the same patient (labeled by patient number), provided by different regression calculation methods. As illustrated, the differences from the predicted outcome for a particular patient using the IOL power recommended by the current regression calculations become more extreme for progressively more myopic eyes (i.e., eyes having an average IOL power predicted of less than 15D) or hyperopic eyes (i.e., eyes having an average IOL power predicted of greater than 25D).
The way in which these deviations from the plano refraction are typically approached is by the optimization of the A constant. Thus, possible bias, as well as, surgical technique can be considered by personalizing this constant. This approach can remove small biases, so that the average population can have zero refraction after surgery. However, the standard deviation is not lowered, meaning that IOL power for those non average eyes is still not correctly predicted.
Postlasik eyes are a particular example of eyes that are not “average,” in part because the corneal power of the post-lasik eye has been modified by lasik surgery. A factor that causes difficulty in obtaining an optimal IOL power outcome for the post-lasik eye is the corneal power (K) in the regression formulas above, which is often incorrectly measured by topographers or keratometers after a lasik procedure. Additionally, the decoupling that occurs between the anterior and posterior corneal radius after lasik makes the effective index calculated for “average” patients inaccurate for postlasik eyes. Thus, it is well known that regression formulas do not typically provide a recommended IOL power that will produce the desired refractive outcome for post-lasik patients and thus regular regression formulas cannot be directly applied to this population without modification.
Moreover, it has been widely reported that the lasik procedure may typically generate large amounts of corneal aberrations. This may be inferred because post-lasik patients typically present higher amounts of corneal aberrations, likely due to the lasik surgery, than would an “average” patient. Such aberrations should not be excluded in IOL power predictions if the desired refractive outcome is to be obtained. Currently, aberrations are not incorporated in regression formulas, which are instead based on paraxial optics as discussed above.
The importance of corneal aberrations in IOL power calculations has been demonstrated in, for example, Application 61/375,657 filed on Aug. 20, 2010 entitled “Apparatus, System and Method for an Empirically-Based, Customized Intraocular Lens Power Calculation”. The ray tracing approach is based on the exact solution of Snell's law for all of the rays passing through the ocular surfaces placed in positions defined by biometric measurements. This is a personalized model, where all the patient's biometric measurements are considered, in contrast with regression formulas, which are based on averages. In this customized model, all corneal aberrations can also be introduced, thus making it applicable for both normal and postlasik patients, for example.
FIG. 2 shows the residual refraction (SE meaning spherical equivalent) achieved by different approaches including the SRK/T as well as the ray tracing approach with and without corneal aberrations for 17 normal patients. Because of the small amount of aberrations, the impact on IOL power calculation is limited.
FIG. 3 shows the improvement in IOL power prediction considering corneal aberration (custom+ab) in the ray tracing approach with respect to the current state of the art in IOL power calculation for postlasik eyes (double K) and also with the same ray tracing procedure without considering corneal wavefront aberrations for 12 patients. FIG. 4 reveals that this improvement is related to the lower standard deviation, so IOL power calculations can be more predictable and accurate when corneal aberrations are considered. FIG. 5 discloses that the improvement in the accuracy of IOL power calculations considering corneal aberrations is mainly due to spherical aberration (z12), since this parameter is highly correlated with the difference in IOL power prediction with and without considering corneal aberrations (CWA_influence).
Although ray tracing may be the most theoretically accurate way to calculate IOL power, all inputs must be very accurate, since there is not an A constant to optimize in case of errors or bias. Another disadvantage of this procedure is that is relatively slow, since the area under the radial MTF is used as an optimized parameter and the computation for this parameter takes time.
Thus, the need exists for an apparatus, system and method that provide greater accuracy in predicting optimal IOL power for particular patients using regression theory, for eyes inside and outside the “average” range.